Non-abelian bosonization in two and three dimensions

Guillou, J.C. Le; Moreno, E.C.; Núñez, Carlos; Schaposnik, F

doi:10.1016/s0550-3213(96)00676-1

Cited by 29 publications

(57 citation statements)

References 43 publications

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“…The other delta completes the identification (70) (These kind of representations are discussed in detail in [22]). One now introduces a Lagrange multiplier a in order to represent the curvature's delta function.…”

Section: The Bosonization Recipementioning

confidence: 73%

Wess–Zumino–Witten and fermion models in noncommutative space

Moreno

Schaposnik

2001

Nuclear Physics B

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We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U (N ) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.

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Section: The Bosonization Recipementioning

confidence: 73%

Wess–Zumino–Witten and fermion models in noncommutative space

Moreno

Schaposnik

2001

Nuclear Physics B

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“…It is well known [32,33,34] that in ordinary commutative geometry the bosonization of N free massless fermions in the fundamental representation of SU(N ) gives rise to a WZW model for a scalar field in SU(N ) plus a free scalar field associated with the U(1) invariance of the fermionic system. In the noncommutative case the bosonization of a single massless Dirac fermion produces a noncommutative U(1) WZW model [35], which becomes free only in the commutative limit.…”

Section: Noncommutative Integrable Sigma Model In 2+1 Dimensionsmentioning

confidence: 99%

Integrable noncommutative sine-Gordon model

et al. 2005

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Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from 2+2 dimensional self-dual U(2) Yang-Mills through a 2+1 dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) → U(1) to U(2) → U(1)×U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.

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“…Our derivation is carried out for the abelian case (and will largely follow [14]) but as we shall see it generalizes immediately to the non-abelian case [15]. In [15] it was shown that a conventional free fermionic theory in 1 + 1 dimensions…”

Section: Bosonization On Noncommutative Spacementioning

confidence: 99%

“…Using the path-integral approach to bosonization [14,13] one starts with the partition function of the free (abelian) fermion theory:…”

Section: Definition Of the Currentmentioning

confidence: 99%

From noncommutative bosonization to S-duality

Núñez

Olsen

Schiappa

2000

J. High Energy Phys.

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We extend standard path-integral techniques of bosonization and duality to the setting of noncommutative geometry. We start by constructing the bosonization prescription for a free Dirac fermion living in the noncommutative plane R 2 θ . We show that in this abelian situation the fermion theory is dual to a noncommutative Wess-Zumino-Witten model.The non-abelian situation is also constructed along very similar lines. We apply the techniques derived to the massive Thirring model on noncommutative R 2 θ and show that it is dualized to a noncommutative WZW model plus a noncommutative cosine potential (like in the noncommutative Sine-Gordon model). The coupling constants in the fermionic and bosonic models are related via strong-weak coupling duality. This is thus an explicit construction of S-duality in a noncommutative field theory.

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Non-abelian bosonization in two and three dimensions

Cited by 29 publications

References 43 publications

Wess–Zumino–Witten and fermion models in noncommutative space

Wess–Zumino–Witten and fermion models in noncommutative space

Integrable noncommutative sine-Gordon model

From noncommutative bosonization to S-duality

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